Fast Algorithm Research Articles

Faster space-efficient STR-IC-LCS computation

One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of A and B. In this paper, we deal with the STR-IC-LCS1 problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A, B, and P, if Z is a longest string satisfying that (1) Z includes P as a substring and (2) Z is a common subsequence of A and B. We present three efficient algorithms for this problem: First, we begin with a space-efficient solution which computes the length of an STR-IC-LCS in O(n2) time and O((ℓ+1)(n−ℓ+1)) space, where ℓ is the length of an LCS of A and B of length n. When ℓ=O(1) or n−ℓ=O(1), then this algorithm uses only linear O(n) space. Second, we present a faster algorithm that works in O(nr/log⁡r+n(n−ℓ+1)) time, where r is the length of P, while retaining the O((ℓ+1)(n−ℓ+1)) space efficiency. Third, we give an alternative algorithm that runs in O(nr/log⁡r+n(n−ℓ′+1)) time with O((ℓ′+1)(n−ℓ′+1)) space, where ℓ′ denotes the STR-IC-LCS length for input strings A, B, and P.

Fast Coding Unit Partitioning Algorithm for Video Coding Standard Based on Block Segmentation and Block Connection Structure and CNN

The recently introduced Video Coding Standard, VVC, presents a novel Quadtree plus Nested Multi-Type Tree (QTMTT) block structure. This structure enables a more flexible block partition and demonstrates enhanced compression performance compared to its predecessor, HEVC. However, The introduction of the new structure has led to a more complex partition search process, resulting in a considerable increase in time complexity. The QTMTT structure yields diverse Coding Unit (CU) block sizes, posing challenges for CNN model inference. In this study, we propose a representation structure termed Block Segmentation and Block Connection (BSC), rooted in texture features. This ensures that partial CU blocks are uniformly represented in size. To address different-sized CUs, various levels of CNN models are designed for prediction. Moreover, we introduce a post-processing method and a multi-thresholding scheme to further mitigate errors introduced by CNNs. This allows for flexible and adjustable acceleration, achieving a trade-off between coding time complexity and performance. Experimental results indicate that, in comparison to VTM-10.0, our “Fast” scheme reduces the average complexity by 57.14% with a 1.86% increase in BDBR. Meanwhile, the “Moderate” scheme reduces average complexity by 50.14% with only a 1.39% increase in BDBR.

A Simple and Fast Algorithm for Generating Correlation Matrices with a Known Average Correlation Coefficient

This article describes a simple and fast algorithm for generating correlation matrices ( R ) with a known average correlation. The algorithm should be useful for researchers desiring plausible R matrices for substantive domains in which average correlations are known (at least approximately). The method is non iterative and it can solve relatively large problems (e.g., generate a 500 × 500 R matrix) in less than a second on a personal computer. It also has didactic value for introducing students to the convex set of feasible R matrices of a fixed dimension. This Euclidean body is called an elliptope. The proposed method exploits the geometry of elliptopes to efficiently generate realistic R matrices with a desired average correlation coefficient. R code for implementing the algorithm (and for reproducing all of the results of this article) is reported in an online supplement.

Fast Beam-Pointing Control Algorithms Based on Deep Learning Models for Moving Target in MWPT

Fast Beam-Pointing Control Algorithms Based on Deep Learning Models for Moving Target in MWPT

FCA-based efficient prediction of effective properties for 3D braided composites considering the effect of strain rate

The existing fast concurrency algorithms are difficult to predict the dynamic mechanical performance of three-dimensional (3D) braided composites from different scales. A modified Finite Element Method Cluster Analysis (FCA) method is employed to address this challenge. The modified FCA method is consisted of an offline and an online stage. In the offline stage, the high-fidelity Representative Unit Cell (RUC) is compressed to form a cluster-based RUC via the k-means method. Additionally, the cluster interaction matrix is calculated. In the online stage, the cluster interaction matrix is updated according to the strain rate levels for predicting the stress–strain curves for the RUC. Based upon the comparison with the data obtained from the Split Hopkinson Pressure Bar (SHPB) experiments, it is found that the modified FCA method can accurately predict the stress–strain curves under different strain rates for RUCs. Additionally, the modified FCA method provides a great improvement on computing efficiency when predicting the dynamic behavior of 3D braided composites.

Location-Aided Fast Beam Tracking Algorithm for Millimeter-Wave V2I

Location-Aided Fast Beam Tracking Algorithm for Millimeter-Wave V2I

High order compact augmented methods for Stokes equations with different boundary conditions

This paper is devoted to fourth order compact schemes and fast algorithms for solving stationary Stokes equations with different boundary conditions numerically. One of the main ideas is to decouple the Stokes equations into three Poisson equations for the pressure and the velocity via the pressure Poisson equation (PPE). The augmented strategy is utilized to provide numerical boundary conditions for the pressure. Different velocity boundary conditions require different interpolation strategies for the augmented methods. The augmented variable is solved by the GMRES method. A new simple and efficient preconditioning strategy has also been developed to accelerate the convergence of the GMRES iteration. Numerical examples presented in this paper confirmed the designed convergence order and the efficiency of the new methods.

Fast, high-order numerical evaluation of volume potentials via polynomial density interpolation

This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the ideas of the density interpolation method for boundary integral operators, the proposed methodology leverages Green's third identity and a local polynomial interpolant of the density function to recast the volume potential as a sum of single- and double-layer potentials and a volume integral with a regularized (bounded or smoother) integrand. The layer potentials can be accurately and efficiently evaluated everywhere in the plane by means of existing methods (e.g. the density interpolation method), while the regularized volume integral can be accurately evaluated by applying elementary quadrature rules. Compared to straightforwardly computing corrections for every singular and nearly-singular volume target, the method significantly reduces the amount of required specialized quadrature by pushing all singular and near-singular corrections to near-singular layer-potential evaluations at target points in a small neighborhood of the domain boundary. Error estimates for the regularization and quadrature approximations are provided. The method is compatible with well-established fast algorithms, being both efficient not only in the online phase but also to set-up. Numerical examples demonstrate the high-order accuracy and efficiency of the proposed methodology; applications to inhomogeneous scattering are presented.

Quantifying the effect of X-ray scattering for data generation in real-time defect detection.

X-ray imaging is widely used for the non-destructive detection of defects in industrial products on a conveyor belt. In-line detection requires highly accurate, robust, and fast algorithms. Deep Convolutional Neural Networks (DCNNs) satisfy these requirements when a large amount of labeled data is available. To overcome the challenge of collecting these data, different methods of X-ray image generation are considered. Depending on the desired degree of similarity to real data, different physical effects should either be simulated or can be ignored. X-ray scattering is known to be computationally expensive to simulate, and this effect can greatly affect the accuracy of a generated X-ray image. We aim to quantitatively evaluate the effect of scattering on defect detection. Monte-Carlo simulation is used to generate X-ray scattering distribution. DCNNs are trained on the data with and without scattering and applied to the same test datasets. Probability of Detection (POD) curves are computed to compare their performance, characterized by the size of the smallest detectable defect. We apply the methodology to a model problem of defect detection in cylinders. When trained on data without scattering, DCNNs reliably detect defects larger than 1.3mm, and using data with scattering improves performance by less than 5%. If the analysis is performed on the cases with large scattering-to-primary ratio (1<SPR<5), the difference in performance could reach 15% (approx. 0.4mm). Excluding the scattering signal from the training data has the largest effect on the smallest detectable defects, and the difference decreases for larger defects. The scattering-to-primary ratio has a significant effect on detection performance and the required accuracy of data generation.

An efficient unstructured quadrilateral-dominated surface mesh generation method for arbitrary geometry with tiny features or crack defects in DiBFM

An efficient unstructured quadrilateral-dominated surface mesh generation algorithm is presented to generate high-quality surface elements for arbitrary geometry with tiny features or crack defects. For complex entities with proximity features, a novel type of meshing template has been proposed to solve the problem of entity boundary fitting of the outside-in grid-based method. The algorithm also works for regions with proximity features, as well as for arbitrary geometry with one or multiple cracks. The procedure incorporates aspects of well-known meshing techniques, but includes some original and efficient processes. The refinement field is constructed according to mesh size, boundary curvature, surface curvature and other geometry features. In order to effectively generate the core mesh, a fast intersection algorithm between topological elements and the solid boundary is established, which improves the efficiency of intersection calculation. The geometry-based techniques are employed for boundary matching of the core mesh. The method has been successfully employed in conjunction with the dual interpolation boundary face method (DiBFM). Several realistic geometries with cracks or proximity features are applied to demonstrate the accuracy and validity of the proposed approach.

Long Short-Term Memory Parameter Optimization Based on Improved Sparrow Search Algorithm for Molten Iron Quality Prediction

Blast furnace (BF) ironmaking is a key process in iron and steel production. Because BF ironmaking is a dynamic time series process, it is more appropriate to use a recurrent neural network for modeling. The long short-term memory (LSTM) network is commonly used to model time series data. However, its model performance and generalization ability heavily depend on the parameter configuration. Therefore, it is necessary to study parameter optimization for the LSTM model. The sparrow search algorithm (SSA) holds advantages over traditional optimization algorithms in several aspects, such as no need for prior knowledge, fewer parameters, fast convergence, and high scalability. However, the algorithm still faces some challenges, such as the tendency to become trapped in the local optimum and the imbalance between global search ability and local search ability. Therefore, on the basis of SSA, this study examined the Levy flight strategy, sine search strategy, and step size factor adjustment strategy to improve it. This algorithm, improved by three strategies, is called the improved sparrow search algorithm (ISSA). Then, the ISSA-LSTM model was established. Furthermore, considering the limitations of SSA in dealing with multi-objective problems, the fast non-dominated sorting genetic algorithm (NSGAII) was introduced, and the ISSA-NSGAII model was established. Finally, experimental validation was performed using real blast furnace operation data, which demonstrated the proposed algorithm’s superiority in parameter optimization for the LSTM model and prediction for real industrial data.

AEKA: FPGA Implementation of Area-Efficient Karatsuba Accelerator for Ring-Binary-LWE-Based Lightweight PQC

Lightweight PQC-related research and development have gradually gained attention from the research community recently. Ring-Binary-Learning-with-Errors (RBLWE)-based encryption scheme (RBLWE-ENC), a promising lightweight PQC based on small parameter sets to fit related applications (but not in favor of deploying popular fast algorithms like number theoretic transform). To solve this problem, in this article, we present a novel implementation of hardware acceleration for RBLWE-ENC based on Karatsuba algorithm, particularly on the field-programmable gate array (FPGA) platform. In detail, we have proposed an area-efficient Karatsuba Accelerator (AEKA) for RBLWE-ENC, based on three layers of innovative efforts. First of all, we reformulate the signal processing sequence within the major arithmetic component of the KA-based polynomial multiplication for RBLWE-ENC to obtain a new algorithm. Then, we have designed the proposed algorithm into a new hardware accelerator with several novel algorithm-to-architecture mapping techniques. Finally, we have conducted thorough complexity analysis and comparison to demonstrate the efficiency of the proposed accelerator, e.g., it involves 62.5% higher throughput and 60.2% less area-delay product (ADP) than the state-of-the-art design for n =512 (Virtex-7 device, similar setup). The proposed AEKA design strategy is highly efficient on the FPGA devices, i.e., small resource usage with superior timing, which can be integrated with other necessary systems for lightweight-oriented high-performance applications (e.g., servers). The outcome of this work is also expected to generate impacts for lightweight PQC advancement.

Analysis of Isomorphism Classes of a Family of Elliptic Curves Over Finite Fields

Doche et al. constructed a family of elliptic curves (DIK elliptic curves) and proposed more efficient tripling formulas leading to a fast scalar multiplication algorithm. In this paper we present a direct method to compute the number of \(\bar{F}\)q-isomorphism classes (isomorphism over \(\bar{F}\)q ) and \(\bar{F}\)q isomorphism classes of DIK family of elliptic curves defined over a finite field \(\bar{F}\)q. We give the explicit formulae for the number of \(\bar{F}\)q-isomorphism and an estimate formulae for the number of isomorphism classes. These result can be used in the elliptic curve cryptosystems.

VAMPyR-A high-level Python library for mathematical operations in a multiwavelet representation.

Wavelets and multiwavelets have lately been adopted in quantum chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few), they provide a framework that narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for multiwavelet calculations (algebra and integral and differential operator application) and exposes the required functionality to write a simple Python code to solve, among others, the Hartree-Fock equations, the generalized Poisson equation, the Dirac equation, and the time-dependent Schrödinger equation up to any predefined precision. In this study, we will outline the main features of multiresolution analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms.

Mora: abundance aware metagenomic read re-assignment for disentangling similar strains

BackgroundTaxonomic classification of reads obtained by metagenomic sequencing is often a first step for understanding a microbial community, but correctly assigning sequencing reads to the strain or sub-species level has remained a challenging computational problem.ResultsWe introduce Mora, a MetagenOmic read Re-Assignment algorithm capable of assigning short and long metagenomic reads with high precision, even at the strain level. Mora is able to accurately re-assign reads by first estimating abundances through an expectation-maximization algorithm and then utilizing abundance information to re-assign query reads. The key idea behind Mora is to maximize read re-assignment qualities while simultaneously minimizing the difference from estimated abundance levels, allowing Mora to avoid over assigning reads to the same genomes. On simulated diverse reads, this allows Mora to achieve F1 scores comparable to other algorithms while having less runtime. However, Mora significantly outshines other algorithms on very similar reads. We show that the high penalty of over assigning reads to a common reference genome allows Mora to accurately infer correct strains for real data in the form of E. coli reads.ConclusionsMora is a fast and accurate read re-assignment algorithm that is modularized, allowing it to be incorporated into general metagenomics and genomics workflows. It is freely available at https://github.com/AfZheng126/MORA.

Hybrid Quantum-classical Search Algorithms

Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover’s algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at least some quantum computation is required to achieve these speedups, the existing bounds do not rule out the possibility of an equally fast hybrid quantum-classical algorithm where most of the computation is classical. In this work, we study such hybrid algorithms, and we show that classical computation, unless it by itself can solve the Search problem, cannot assist quantum computation. In addition, we generalize this result to algorithms with subconstant success probabilities.

A Fast Factorized Back-Projection Algorithm Based on Range Block Division for Stripmap SAR

Fast factorized back-projection (FFBP) is a classical fast time-domain technique that has garnered significant success in spotlight synthetic aperture radar (SAR) signal processing. The algorithm’s efficiency has been extended to stripmap SAR through integral aperture determination and full-aperture data block processing while retaining its computational efficiency. However, the above method is only operated in the azimuth direction, and the computing efficiency needs to be urgently improved in the actual processing process. This paper proposes a fast factorized back-projection algorithm for stripmap SAR imaging based on range block division. The echo data are divided into multiple subblocks in the range direction, and FFBP processing is applied separately to each full-aperture subblock, further enhancing computational efficiency. The paper analyzes the algorithm’s principles, underscores the necessity of integral aperture determination and full-aperture data block processing, provides specific implementation steps, and applies the algorithm to point target simulation and experimental data from a vehicle-mounted ice radar. The experiments validate the algorithm’s efficiency in stripmap SAR imaging.

Research on a Fast Image-Matching Algorithm Based on Nonlinear Filtering

Computer vision technology is being applied at an unprecedented speed in various fields such as 3D scene reconstruction, object detection and recognition, video content tracking, pose estimation, and motion estimation. To address the issues of low accuracy and high time complexity in traditional image feature point matching, a fast image-matching algorithm based on nonlinear filtering is proposed. By applying nonlinear diffusion filtering to scene images, details and edge information can be effectively extracted. The feature descriptors of the feature points are transformed into binary form, occupying less storage space and thus reducing matching time. The adaptive RANSAC algorithm is utilized to eliminate mismatched feature points, thereby improving matching accuracy. Our experimental results on the Mikolajcyzk image dataset comparing the SIFT algorithm with SURF-, BRISK-, and ORB-improved algorithms based on the SIFT algorithm conclude that the fast image-matching algorithm based on nonlinear filtering reduces matching time by three-quarters, with an overall average accuracy of over 7% higher than other algorithms. These experiments demonstrate that the fast image-matching algorithm based on nonlinear filtering has better robustness and real-time performance.

TrieDedup: a fast trie-based deduplication algorithm to handle ambiguous bases in high-throughput sequencing

BackgroundHigh-throughput sequencing is a powerful tool that is extensively applied in biological studies. However, sequencers may produce low-quality bases, leading to ambiguous bases, ‘N’s. PCR duplicates introduced in library preparation are conventionally removed in genomics studies, and several deduplication tools have been developed for this purpose. Two identical reads may appear different due to ambiguous bases and the existing tools cannot address ‘N’s correctly or efficiently.ResultsHere we proposed and implemented TrieDedup, which uses the trie (prefix tree) data structure to compare and store sequences. TrieDedup can handle ambiguous base ‘N’s, and efficiently deduplicate at the level of raw sequences. We also reduced its memory usage by approximately 20% by implementing restrictedDict in Python. We benchmarked the performance of the algorithm and showed that TrieDedup can deduplicate reads up to 270-fold faster than pairwise comparison at a cost of 32-fold higher memory usage.ConclusionsThe TrieDedup algorithm may facilitate PCR deduplication, barcode or UMI assignment, and repertoire diversity analysis of large-scale high-throughput sequencing datasets with its ultra-fast algorithm that can account for ambiguous bases due to sequencing errors.

A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition

A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition